| Line 27: | Line 27: | ||
<math> H(s) = \int_{-\infty}^{\infty} e^{-j*w*k} * 2\delta(\tau) d\tau </math> | <math> H(s) = \int_{-\infty}^{\infty} e^{-j*w*k} * 2\delta(\tau) d\tau </math> | ||
| − | + | 2*1 = 2 | |
| − | + | H(s) = 2 | |
Revision as of 16:22, 25 September 2008
CT LTI sytem
An example system would be:
y(t) = 2*x(t)
Part A: The unit impulse response and system function H(s)
The unit impulse response:
$ x(t) \to \delta(t) * h(t) = 2*\delta(t) $
The system function, H(s) derivation:
$ y(t) = \int_{-\infty}^{\infty} x(\tau) * h(\tau) *d\tau $
$ y(t) = \int_{-\infty}^{\infty} e^{-j*w(t-k)} * 2\delta(\tau) *d\tau $
$ y(t) = e^{j*w*t} \int_{-\infty}^{\infty} e^{-j*w*k} * 2\delta(\tau) * d\tau $
$ H(s) = \int_{-\infty}^{\infty} e^{-j*w*k} * 2\delta(\tau) d\tau $
2*1 = 2
H(s) = 2
